OSCILLATORY BEHAVIOR OF EVEN ORDER MIXED NEUTRAL DIFFERENTIAL EQUATIONS

In this paper,we shall consider a class of even order mixed neutral differential equations. Some new oscillations criteria of the solutions are obtained.     

中立型时滞差分方程解的渐近性

给出了中立型时滞差分方程△（ｘｎ＋ｐｘｎ－ｋ）＋ｑｎｆ（ｘｎ－ｍ）＝０一切非振动解趋于零（ｎ→∞）的充分条件，证明了方程（Ｅ）一切解振动的两个新的定理。     

二阶差分方程解的振动性与渐近性

本文研究了二阶差分方程Δ(a     

ASYMPTOTIC BEHAVIOR OFNONOSCILLATORY SOLUTIONS OF SECOND ORDER NEUTRAL NONLINEAR DIFFERENCE EQUATIONS

1IntroductionConsiderthesecondorderneutralnonlineardifferenceequationwherenEN(no)={no,no 1,'.}(noisanonnegativeinteger),AE{--l,1},AistheforworddifferenceoperatordefinedbyAx.=xu 1--xu.Inrecentyearssthequalitativepropertiesofthesolutionsofsecondorderneutraldifferenceequationswereconsideredinanumberofpapers[1--10].Allthepapersmentioned,however,alwaysassumethatqn50foralllargen.Inthispaperouraimistostudytheasymptoticbehaviorofnonoscillatorysolutionsof(l)whenqn20foralllargen.Byasolutionof(1)weme…     

OSCILLATION CRITERIA FOR SECOND ORDER DIFFERENCE EQUATIONS OF NEUTRAL TYPE WITH MIXED ARGUMENTS

In this paper, we establish some new oscillation criteria for second order difference equations of neutral type with mixed arguments. We extend some known oscillation criteria for second order difference equations.     

AN OSCILLATION CRITERION FOR EVEN ORDER NEUTRAL DIFFERENCE EQUATIONS

An oscillation criterion is obtained for even order neutral type differenceequations of the following formΔ~m(x_n+α_nx_(n-т))+f(n,x_n,x_(n-σ))=0,n=n_0,n_0+1,…,where m≥2 is even, n_0 is a nonnegative integer, Δ is the forward differenceoperator defined by Δx_n=x_(n+1)-x_n, and for i≥1, Δ~i is the i~(th)-order forwarddifference operator defined by Δ~ix_n=Δ(Δ~(i-1)x_n),т and σ are positive integers.     

一类非线性中立型差分方程解的振动性

本文我们证明了下列两个差分方程Δ（ｘｎ － ｘｎ－ ｋ）α＋ ｑｎｆ（ｘｎ－ Ｔ） ＝ ０Δ（Δｙｎ－ １）α＋ ｋ－ αｑｎｆ（ｙｎ） ＝ ０振动的等价性．其中ｑｎ０,ｋ,Ｔ为正整数,α为两奇数之商,ｆ∈Ｃ（Ｒ,Ｒ）是非减的并满足ｘｆ（ｘ）＞ ０（ｘ≠０）．获得了这些方程振动的一些充分条件．     

NEW OSCILLATION CRITERIA FOR FIRST ORDER NEUTRAL DIFFERENCE EQUATIONS

1 IntroductionIn recent yearss those who were interested in studying the neutral differenceequation were growing more and more. The oscillation and nonoscillation ofsolutions of neutral difference equation have been extensively investigated (see[l][2][3]).Our aim in this paper is to obtain some sufficient conditions for the oscillation of all solutions of neutral difference equationA(x(n) -- p(n)x(n -- m)) Q(n)x(n -- k) = 0, n 2 no, (1)wherep(n), Q(n) 6 C({no, no 1,' .}, R ), m > 0, and…     

OSCILLATION THEOREMS FOR SECOND ORDER NEUTRAL DIFFERENCE EQUATIONS

The aim of this paper is to study the oscillation of second order neutral difference equations.Our results are based on the new comparison theorems,that reduce the problem of the oscillation of the second order equation to that of the first order equation.The comparison principles obtained essentially simplify the examination of the equations.     

高阶中立型差分方程的振动性及其非振动解的渐近性态

本文给出了高阶非线性中立型时滞差分方程△＾ｄ（ｘ（ｎ－Ｐ（ｎ）ｘ（ｎ－ｋ））＋ｇ（ｎ）ｆ（ｘ（ｍ－ｌ）＝０振动的一个充分条件,同时以给出该方程的非振动解趋于零的判据。     

CONVERGENCE OF SOLUTIONS OF CERTAIN SYSTEM OF THIRD ORDER NON-LINEAR ORDINARY DIFFERENTIAL EQUATIONS

The object of this paper is to give an n-dimensional analogue of a convergence result of Tejumola [8] for some third-order differential equations. The result extends earlier results of Afuwape [1] and Ezeilo [4] to some system of third-order differential equations.     

非线性中立型时滞差分方程解的渐近性

本文考虑非线性中立型差分方程△m(Xn-m 1 Pn-m 1Xn-m 1-k) f(n,Xn-l) 0解的振动性和渐近性,所得结果推广了文献中的有关定理．     

一类非线性中立型差分方程的振动性(英文)

考虑一类非线性中立型差分方程Δ（ｘｎ － ｐｎｘｎ－ ｋ） ＋ ｑｎｆ（ｘｎ－ ｌ） ＝ ０ （）我们得到了其所有解振动的几个充分条件．     

高阶非线性中立型时滞微分方程的渐近性态

本文研究一类高阶非线性中立型时滞微分方程解的渐近性态。这些结果推广了某些已知的结论。     

OSCILLATION CRITERIA OF SOLUTIONS OF NONLINEAR DIFFERENCE EQUATIONS OF SECOND ORDER

Oscillatory behavior of solutions of second order nonlinear difference equation is studied. Oscillation criteria for its solutions are given. Examples are given in the text to illustrate the results.     

ASYMPTOTICS AND OSCILLATION FOR FIRST ORDER MIXED NEUTRAL DIFFERENTIAL EQUATIONS

1IntroductionConsidertheneutraldifferentialequationswherepiERfori=l,2,...,m;o相似文献   

一类二阶非线性微分方程解的振动性与渐近性

本文研究了二阶非线性微分方程的解的振动性与渐近性.其中σ是一个偶数与奇数的正商.所得的结果是新的,其中之一修正了Wong的结果.     

二阶非线性中立型微分方程的振动性

利用广义Riccati变换和权函数积分平均技巧,建立了非线性时滞中立型方程:[r(t)(x(t)-p(t)x(t-τ))']'+q(t)f(x(t-δ))h(x'(t))=0的振动准则,其中τ和δ是非负常数,a,p,q∈C([to,∞),R),f和h∈C(R,R).这些结果补充了大量存在性结论和处理以前结果不能解决的问题.特别地,以实例说明本文结果是实质性推广.     

又一类三阶中立型分布时滞微分方程的振动定理

本文研究三阶中立型分布时滞微分方程的振动问题.利用Riccati变换技巧和积分平均方法,获得了方程每一解振动或者收敛到零点的新准则,最后,给出了说明所得结果应用的例子.     

高阶混合中立型微分方程解的振动性

本文研究奇数阶混合类型的中立型微分方程[x(t)+cx(t-h)+c*x(t+h*)](n)=qx(t-g)+px(t+g*),这里c,c*,g,g*,h,h*,p和q是实常数,得到关于解振动的一些新的判别准则.本文结果改进了GraceS.R.的全部定理.